“It has been an amazing journey to play for my childhood club since I was 14,” he said via his official Twitter account.
“I would like to thank Arsene Wenger for giving me the chance to start my career and fulfil a dream!
“Now it’s time for the next chapter with West Bromwich Albion and I can’t wait to get started with the boys!”
Pulis added to West Brom’s official website: “We’ve now got a deal which I think is right for the club and I’m really pleased to add a player of this quality and experience to our group.
“Kieran’s a good age and has made over 200 appearances for Arsenal, represented his country and has Premier League and Champions League experience.
“To add these qualities to our squad is exactly what we’re looking for.”
The 27-year-old signed a four-year contract at The Hawthorns, where he will wear the number three shirt.
Gibbs, who made his debut for the Gunners in 2007, made 229 appearances in total in all competitions.